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At least 721 records · Page 40

Co-Optimization of Velocity and Charge-Depletion for Plug-In Hybrid Electric Vehicles: Accounting for Acceleration and Jerk Constraints

Abstract Recent advances in vehicle connectivity and automation technologies promote advanced control algorithms that co-optimize the longitudinal dynamics and powertrain operation of hybrid electric vehicles. Typically, a sequential optimization with the vehicle dynamics optimized followed by powertrain optimization is adopted to manage a number of complexities such as the inherent mixed-integer nature of the hybrid powertrain, the numerous state and control variables, the differing time scales of vehicle and powertrain subsystems, time-varying state constraints, and large horizon lengths. Instead, we solve the offline optimization problem in a centralize manner assuming exact knowledge of the lead vehicle's position over the entire trip by applying a discrete-time single shooting-based numerical approach, Discrete Mixed-Integer Shooting (DMIS), including a linearly increasing computational complexity to the problem horizon. In particular, the hierarchical problem structure is exploited to decompose the computationally intensive Hamiltonian minimization step into a set of low-dimensional optimizations. DMIS allows us to compute the direct fuel minimization problem including the vehicle and powertrain dynamics in a centralized manner to its full horizon while systematically tuning weighting factors that penalize passenger discomfort. For the first time, this study reveals that practically implemented sequential optimization exhibits similar fuel optimality as co-optimization when a certain level of passenger comfort is required.

Automation & Control Systems↗

TU-EF-204-03: Task-Based KV and MAs Optimization for Radiation Dose Reduction in CT: From FBP to Statistical Model-Based Iterative Reconstruction (MBIR)

Purpose: The introduction of the highly nonlinear MBIR algorithm to clinical CT systems has made CNR an invalid metric for kV optimization. The purpose of this work was to develop a task-based framework to unify kV and mAs optimization for both FBP- and MBIR-based CT systems. Methods: The kV-mAs optimization was formulated as a constrained minimization problem: to select kV and mAs to minimize dose under the constraint of maintaining the detection performance as clinically prescribed. To experimentally solve this optimization problem, exhaustive measurements of detectability index (d’) for a hepatic lesion detection task were performed at 15 different mA levels and 4 kV levels using an anthropomorphic phantom. The measured d’ values were used to generate an iso-detectability map; similarly, dose levels recorded at different kV-mAs combinations were used to generate an iso-dose map. The iso-detectability map was overlaid on top of the iso-dose map so that for a prescribed detectability level d’, the optimal kV-mA can be determined from the crossing between the d’ contour and the dose contour that corresponds to the minimum dose. Results: Taking d’=16 as an example: the kV-mAs combinations on the measured iso-d’ line of MBIR are 80–150 (3.8), 100–140 (6.6), 120–150 (11.3), and 140–160 (17.2), where values in the parentheses are measured dose values. As a Result, the optimal kV was 80 and optimal mA was 150. In comparison, the optimal kV and mA for FBP were 100 and 500, which corresponded to a dose level of 24 mGy. Results of in vivo animal experiments were consistent with the phantom results. Conclusion: A new method to optimize kV and mAs selection has been developed. This method is applicable to both linear and nonlinear CT systems such as those using MBIR. Additional dose savings can be achieved by combining MBIR with this method. This work was partially supported by an NIH grant R01CA169331 and GE Healthcare. K. Li, D. Gomez-Cardona, M. G. Lubner: Nothing to disclose. P. J. Pickhardt: Co-founder, VirtuoCTC, LLC Stockholder, Cellectar Biosciences, Inc. G.-H. Chen: Research funded, GE Healthcare; Research funded, Siemens AX.

60 APPLIED LIFE SCIENCES↗

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗

Optimization Plugin Library

The Optimization Plugin library ("op") is a lightweight general optimization solver interface. The primary purpose of op is to simplify the process of integrating different optimization solvers (serial or parallel) with scalable parallel physics engines. By design it has several features that help make this a reality. The core abstraction interface was developed to encompass a large class of optimization problems in an optimizer-agnostic way. This enables us to describe the optimization problem once and then use a variety of supported "op" optimizers with ideally no code-changes. The abstraction interface is made up of lightweight wrappers that make it easy to integrate with existing simulation codes. This makes integration less intrusive and should minimize changes to existing physics codes. The "op" interface includes an assortment of utility methods that help specify parallel communication patterns as well as methods to convert from optimization-specific interfaces to the more general "op" interface. Lastly a dynamic library linking interface is provided to allow for use of proprietary optimization engines without explicit reference in the source code, along with standard shared library interfaces for opensource engines.

Jekel, CharlesF↗

Signatures of optimal codon usage in metabolic genes inform budding yeast ecology

Reverse ecology is the inference of ecological information from patterns of genomic variation. One rich, heretofore underutilized, source of ecologically relevant genomic information is codon optimality or adaptation. Bias toward codons that match the tRNA pool is robustly associated with high gene expression in diverse organisms, suggesting that codon optimization could be used in a reverse ecology framework to identify highly expressed, ecologically relevant genes. To test this hypothesis, we examined the relationship between optimal codon usage in the classic galactose metabolism ( GAL ) pathway and known ecological niches for 329 species of budding yeasts, a diverse subphylum of fungi. We find that optimal codon usage in the GAL pathway is positively correlated with quantitative growth on galactose, suggesting that GAL codon optimization reflects increased capacity to grow on galactose. Optimal codon usage in the GAL pathway is also positively correlated with human-associated ecological niches in yeasts of the CUG-Ser1 clade and with dairy-associated ecological niches in the family Saccharomycetaceae. For example, optimal codon usage of GAL genes is greater than 85% of all genes in the genome of the major human pathogen Candida albicans (CUG-Ser1 clade) and greater than 75% of genes in the genome of the dairy yeast Kluyveromyces lactis (family Saccharomycetaceae). We further find a correlation between optimization in the GAL actose pathway genes and several genes associated with nutrient sensing and metabolism. This work suggests that codon optimization harbors information about the metabolic ecology of microbial eukaryotes. This information may be particularly useful for studying fungal dark matter—species that have yet to be cultured in the lab or have only been identified by genomic material.

59 BASIC BIOLOGICAL SCIENCES↗

Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems

Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading candidates for demonstrating quantum advantage in the near term. QAOA is a variational hybrid quantum-classical algorithm for approximately solving combinatorial optimization problems. The quality of the solution obtained by QAOA for a given problem instance depends on the performance of the classical optimizer used to optimize the variational parameters. In this paper, we formulate the problem of finding optimal QAOA parameters as a learning task in which the knowledge gained from solving training instances can be leveraged to find high-quality solutions for unseen test instances. To this end, we develop two machine-learning-based approaches. Our first approach adopts a reinforcement learning (RL) framework to learn a policy network to optimize QAOA circuits. Our second approach adopts a kernel density estimation (KDE) technique to learn a generative model of optimal QAOA parameters. In both approaches, the training procedure is performed on small-sized problem instances that can be simulated on a classical computer; yet the learned RL policy and the generative model can be used to efficiently solve larger problems. Furthermore, extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our proposed RL- and KDE-based approaches reduce the optimality gap by factors up to 30.15 when compared with other commonly used off-the-shelf optimizers.

97 MATHEMATICS AND COMPUTING↗

Pressurized Water Reactor Gadolinia Pin Location Optimization

This report presents the results of lattice optimization studies performed to find optimum locations for gadolinia burnable absorber (BA) rods in pressurized water reactor (PWR) lattice fuel designs. Initial excess reactivity suppression allows core designers to further improve operational economics by extending cycle length. Gadolinia BAs are commonly used in boiling water reactor assembly designs for this purpose. In recent years, gadolinia absorbers have been used in PWR designs owing to their longer effectiveness for reactivity suppression compared with common BAs used in PWR assemblies. This report examines the optimum gadolinia pin placement in 17 × 17 PWR lattices at different fuel and gadolinia concentrations for optimized lattice performance, using the SCALE/Polaris lattice physics code. The completed work is continuation of the Light Water Reactor LEU+ Lattice Optimization (ORNL/TM-2021/2366) project. An optimization driver called the metaheuristic optimization tool (MOT) is used to automate domain space exploration and optimization of the lattice designs. Heuristics from previous light-water reactor (LWR) lattice optimization studies were used to construct the objective function and define the domain space for optimization. This work successfully demonstrated that the optimization algorithms of MOT can generate feasible, nonproprietary PWR lattice designs with gadolinia.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Intrusive Uncertainty Quantification and Optimal Experiment Design in the Open-Source Pyomo Ecosystem

This contribution describes ParmEst and Pyomo.DoE, two pillars of the open-source Python-based Pyomo ecosystem for computational optimization with (partial differential) algebraic equation mathematical models. Specifically, ParmEst facilitates intrusive frequentist parameter estimation (PE) and uncertainty quantification (UQ) through built-in features, such as covariance matrix estimation, bootstrapping, and likelihood ratio tests. Complementary, Pyomo.DoE enables optimal experiment design by maximizing various metrics of the Fisher information matrix, such as A-optimality (trace), D-optimality (determinant), E-optimality (minimum eigenvalue), and ME-optimality (condition number). ParmEst and Pyomo.DoE can solve high-dimensional optimization problems by leveraging the model structure and exact derivative information. Finally, we will discuss future opportunities to integrate PE and UQ capabilities with optimization under uncertainty, including robust optimization with non-convex models via PyROS.

97 MATHEMATICS AND COMPUTING↗

Modeling and Optimization of a Nuclear Integrated Energy System for the Remote Microgrid on El Hierro

Nuclear microreactors are a potential technology to provide heat and electricity for remote microgrids. There is potential for the microgrid on the island of El Hierro to use a microreactor, within an integrated energy system (IES), to generate electricity and provide desalinated water. This work proposes a workflow for optimizing and analyzing IESs for microgrids. In this study, an IES incorporating a microreactor, thermal energy storage (TES) system, combined heat and power plant, and a thermal desalination plant was designed, optimized, and analyzed using Idaho National Laboratory’s Framework for Optimization of Resources and Economics (FORCE) toolset. The optimization tool, Holistic Energy Resource Optimization Network (HERON), was used to determine the optimal capacity sizes and dispatch for the reactor and thermal energy storage systems to meet demand. The optimized reactor and TES sizes were found to be 11.61 MWth and 58.47 MWhth, respectively, when optimizing the IES to replace 95% of the island’s existing diesel generation needs. A dynamic model of the system was created in the Modelica language, using models from the HYBRID repository, to analyze and verify the dispatch from the optimizer. The dynamic model was able to meet the ramp rates while maintaining reactor power with minimal control adjustments.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Coupled wind turbine design and layout optimization with nonhomogeneous wind turbines

Abstract. In this study, wind farms were optimized to show the benefit of coupling complete turbine design and layout optimization as well as including two different turbine designs in a fixed 1-to-1 ratio in a single wind farm. For our purposes, the variables in each turbine optimization include hub height, rotor diameter, rated power, tower diameter, tower shell thickness, and implicit blade chord-and-twist distributions. A 32-turbine wind farm and a 60-turbine wind farm were both considered, as well as a variety of turbine spacings and wind shear exponents. Structural constraints as well as turbine costs were considered in the optimization. Results indicate that coupled turbine design and layout optimization is superior to sequentially optimizing turbine design, then turbine layout. Coupled optimization results in an additional 2 %–5 % reduction in the cost of energy compared to optimizing sequentially for wind farms with turbine spacings of 8.5–11 rotor diameters. Smaller wind farms benefit even more from coupled optimization. Furthermore, wind farms with closely spaced wind turbines can greatly benefit from nonuniform turbine design throughout the farm. Some of these wind farms with heterogeneous turbine design have an additional 10 % cost-of-energy reduction compared to wind farms with identical turbines throughout the farm.

Stanley, Andrew P. J.↗

Roofline Analysis in the Intel® Advisor to Deliver Optimized Performance for applications on Intel® Xeon Phi™ Processor

In this session we show, in two case studies, how the roofline feature of Intel Advisor has been utilized to optimize the performance of kernels of the XGC1 and PICSAR codes in preparation for Intel Knights Landing architecture. The impact of the implemented optimizations and the benefits of using the automatic roofline feature of Intel Advisor to study performance of large applications will be presented. This demonstrates an effective optimization strategy that has enabled these science applications to achieve up to 4.6 times speed-up and prepare for future exascale architectures. # Goal/Relevance of Session The roofline model [1,2] is a powerful tool for analyzing the performance of applications with respect to the theoretical peak achievable on a given computer architecture. It allows one to graphically represent the performance of an application in terms of operational intensity, i.e. the ratio of flops performed and bytes moved from memory in order to guide optimization efforts. Given the scale and complexity of modern science applications, it can often be a tedious task for the user to perform the analysis on the level of functions or loops to identify where performance gains can be made. With new Intel tools, it is now possible to automate this task, as well as base the estimates of peak performance on measurements rather than vendor specifications. The goal of this session is to demonstrate how the roofline feature of Intel Advisor can be used to balance memory vs. computation related optimization efforts and effectively identify performance bottlenecks. A series of typical optimization techniques: cache blocking, structure refactoring, data alignment, and vectorization illustrated by the kernel cases will be addressed. # Description of the codes ## XGC1 The XGC1 code [3] is a magnetic fusion Particle-In-Cell code that uses an unstructured mesh for its Poisson solver that allows it to accurately resolve the edge plasma of a magnetic fusion device. After recent optimizations to its collision kernel [4], most of the computing time is spent in the electron push (pushe) kernel, where these optimization efforts have been focused. The kernel code scaled well with MPI+OpenMP but had almost no automatic compiler vectorization, in part due to indirect memory addresses and in part due to low trip counts of low-level loops that would be candidates for vectorization. Particle blocking and sorting have been implemented to increase trip counts of low-level loops and improve memory locality, and OpenMP directives have been added to vectorize compute-intensive loops that were identified by Advisor. The optimizations have improved the performance of the pushe kernel 2x on Haswell processors and 1.7x on KNL. The KNL node-for-node performance has been brought to within 30% of a NERSC Cori phase I Haswell node and we expect to bridge this gap by reducing the memory footprint of compute intensive routines to improve cache reuse. ## PICSAR is a Fortran/Python high-performance Particle-In-Cell library targeting at MIC architectures first designed to be coupled with the PIC code WARP for the simulation of laser-matter interaction and particle accelerators. PICSAR also contains a FORTRAN stand-alone kernel for performance studies and benchmarks. A MPI domain decomposition is used between NUMA domains and a tile decomposition (cache-blocking) handled by OpenMP has been added for shared-memory parallelism and better cache management. The so-called current deposition and field gathering steps that compose the PIC time loop constitute major hotspots that have been rewritten to enable more efficient vectorization. Particle communications between tiles and MPI domain has been merged and parallelized. All considered, these improvements provide speedups of 3.1 for order 1 and 4.6 for order 3 interpolation shape factors on KNL configured in SNC4 quadrant flat mode. Performance is similar between a node of cori phase 1 and KNL at order 1 and better on KNL by a factor 1.6 at order 3 with the considered test case (homogeneous thermal plasma).

97 MATHEMATICS AND COMPUTING↗

Multi-scale and multi-physics analysis, design optimization, and experimental validation of heat exchangers utilizing high performance, non-round tubes

Air-to-refrigerant heat exchangers (HXs) are fundamental components in HVAC&R systems, and considerable research has been dedicated designing continually smaller, lighter, and more efficient HX designs. In recent years, researchers have leveraged advancements in Computational Fluid Dynamics (CFD), Finite Element Analysis (FEA), and optimization algorithms to consider primary tube shape and topology optimization to design highly compact, high performance HXs for a multitude of applications. In this research, we present a computationally efficient, comprehensive, multi-scale, and multi-physics analysis and optimization method for air-to-refrigerant HXs featuring automated CFD and FEA simulations and approximation-assisted optimization. This methodology was utilized to design HXs with shape-optimized, non-round tubes which outperform current state-of-the-art tube-fin HXs without compromising structural integrity. The optimal HXs were shown to deliver similar thermal performance to the baseline HXs while also achieving more than 20% reductions in airside pressure drop and core envelope volume and more than 30% reduction in internal volume. Comprehensive experimental validation of the optimization methodology was conducted through the testing of two prototypes in a standardized wind tunnel facility under multiple operating conditions. For prototype #1 under dry evaporator conditions, the predicted heat load agreed within ± 10% of measured values and the predicted airside pressure drop agreed within ± 30%, while for dehumidifying conditions, the predicted sensible and latent heat loads agreed within ± 10% and ± 20% of the measured values, respectively. For prototype #2, the predicted condenser heat load agreed within ± 3.0% of measured values, and the predicted airside pressure drop agreed within ± 27%. The acceptable agreement between simulation and experimental results for the present application highlights the flexibility of the novel optimization methodology to design next generation HXs with improved performance and reduced volume, weight, and environmental impact.

42 ENGINEERING↗

Variable-fidelity multipoint aerodynamic shape optimization with output-based adapted meshes

This work presents a method to control the discretization error in multipoint aerodynamic shape optimization using output-based adapted meshes. The meshes are adapted via adjoint-based error estimates, taking into account both the objective and constraint output errors. A multi-fidelity optimization framework is then developed by taking advantage of the variable fidelity offered by adaptive meshes. The objective functional and its sensitivity at each design point (operating condition) are first evaluated on the same initial coarse mesh, which is then subsequently adapted for each design point individually as the shape optimization proceeds. The effort to set up the optimization is minimal since the initial mesh can be fairly coarse and easy to generate. As the shape approaches the optimal design, the mesh at each design point becomes finer, in regions necessary for that particular operating condition. The multi-fidelity framework is tightly coupled with the objective error estimation to ensure the optimization accuracy at each fidelity. Computational savings arise from a reduction of the mesh size when the design is far from optimal and avoiding an exhaustive search on low-fidelity meshes. The proposed method is demonstrated on multipoint drag minimization problems of a transonic airfoil with lift and area constraints. Improved accuracy and efficiency are shown compared to traditional fixed-fidelity optimization with a fixed computational mesh.

42 ENGINEERING↗

Development of novel dynamic machine learning-based optimization of a coal-fired power plant

The increasing fraction of intermittent renewable energy in the electrical grid is resulting in coal-fired boilers now routinely ramp up and down. The current state-of-the-art operation for such boilers is to apply steady-state, neural network-based optimization to make control decisions in real-time, and this report demonstrates the feasibility of extending this to dynamic, neural network-based optimization using a long short-term memory neural network. A simplified numerical simulation of a t-fired coal boiler and supporting equipment is used to represent a real plant subjected to both steady-state, neural network-based optimization and dynamic, neural network-based optimization. Using the same intervals and a particle swarm optimization algorithm, the dynamic optimization outperforms the steady-state optimization and realizes up to 4.58% improvement in thermal efficiency. Dynamic optimization with a long short-term memory neural network is shown to both be feasible and beneficial for operation of a coal-fired boiler under changing load.

42 ENGINEERING↗

An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems

We report the fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high-order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain is transformed into one on a fixed reference domain by the introduction of a time-dependent mapping that encapsulates the domain deformation and parametrization, resulting in an Arbitrary Lagrangian–Eulerian form of the governing equations. A high-order discontinuous Galerkin method is used to discretize the transformed equation in space and a high-order diagonally implicit Runge–Kutta scheme is used for the temporal discretization. Quantities of interest that take the form of space–time integrals are discretized in a solver-consistent manner. The corresponding fully discrete adjoint method is used to compute exact gradients of quantities of interest along the manifold of solutions of the fully discrete conservation law. These quantities of interest and their gradients are used in the context of gradient-based PDE-constrained optimization. The adjoint method is used to solve two optimal shape and control problems governed by the isentropic, compressible Navier–Stokes equations. The first optimization problem seeks the energetically optimal trajectory of a 2D airfoil given a required initial and final spatial position. The optimization solver, driven by gradients computed via the adjoint method, reduced the total energy required to complete the specified mission nearly an order of magnitude. The second optimization problem seeks the energetically optimal flapping motion and time-morphed geometry of a 2D airfoil given an equality constraint on the x-directed impulse generated on the airfoil. The optimization solver satisfied the impulse constraint to greater than 8 digits of accuracy and reduced the required energy between a factor of 2 and 10, depending on the value of the impulse constraint, as compared to the nominal configuration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm

Directed self-assembly (DSA) of block copolymers (BCPs) is one of the most promising developments in the cost-effective production of nanoscale devices. The process makes use of the natural tendency for BCP melts to form nanoscale structures upon phase separation. The phase separation can be directed through the use of chemically patterned substrates to promote the formation of morphologies that are essential to the production of semiconductor devices. Moreover, the design of substrate pattern can be formulated as an optimization problem for which we seek optimal substrate designs that effectively produce given target morphologies. In this paper, we adopt a phase field model given by a nonlocal Cahn–Hilliard partial differential equation (PDE) based on the minimization of the Ohta–Kawasaki free energy, and present an efficient PDE-constrained optimization framework for the optimal design problem. The design variables are the locations of circular- or strip-shaped guiding posts that are used to model the substrate chemical pattern. To solve the ensuing optimization problem, we propose a variant of an inexact Newton conjugate gradient algorithm tailored to this problem. Additionally, we demonstrate the effectiveness of our computational strategy on numerical examples that span a range of target morphologies. Owing to our second-order optimizer and fast state solver, the numerical results demonstrate five orders of magnitude reduction in computational cost over previous work. The efficiency of our framework and the fast convergence of our optimization algorithm enable us to rapidly solve the optimal design problem in not only two, but also three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗

Dynamic machine learning-based optimization algorithm to improve boiler efficiency

With decreasing computational costs, improvement in algorithms, and the aggregation of large industrial and commercial datasets, machine learning is becoming a ubiquitous tool for process and business innovations. Machine learning is still lacking applications in the field of dynamic optimization for real-time control. This work presents a novel framework for performing constrained dynamic optimization using a recurrent neural network model combined with a metaheuristic optimizer. The framework is designed to augment an existing control system and is purely data-driven, like most industrial Model Predictive Control applications. Several recurrent neural network models are compared as well as several metaheuristic optimizers. Hyperparameters and optimizer parameters are tuned with parameter sweeps, and the resulting values are reported. Further, the best parameters for each optimizer and model combination are demonstrated in closed-loop control of a dynamic simulation, and several recommendations are made for generalizing this framework to other systems. Up to 0.953% improvement is realized over the non-optimized case for a simulated coal-fired boiler. While this is not a large improvement in percentage, the total economic impact is $991,000 per year, and this study builds a foundation for future machine learning with dynamic optimization.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Quantum approximate multi-objective optimization

The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗